The value of compressibility factor of van der Waals gas at critical point is?a) 8/27b) 27/8c) 3/8d) I8/3
Question
The value of compressibility factor of van der Waals gas at critical point is?a) 8/27b) 27/8c) 3/8d) I8/3
Solution
The compressibility factor (Z) of a van der Waals gas at the critical point is given by the formula:
Zc = PcVc/(RTc)
Where:
- Pc is the critical pressure
- Vc is the critical volume
- R is the universal gas constant
- Tc is the critical temperature
For a van der Waals gas, these critical constants are given by:
Pc = a/(27b^2) Vc = 3b Tc = 8a/(27b*R)
Substituting these values into the formula for Zc gives:
Zc = (a/(27b^2))(3b)/(8a/(27bR)) = 3/8
So, the compressibility factor of a van der Waals gas at the critical point is 3/8. Therefore, the correct answer is c) 3/8.
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